## Modelling in Natural Sciences: Design, Validation and Case StudiesZwar weifl ich viei, doch macht' ich alles wissen 1 Goethe, Faust 1, Vers 601 Man has always recognized his limitations as a challenge to strive for new hori zons. Today, technical progress enables him to realize this ambition; one of the means are models granting new insights into phenomena or problems which can not be observed or (otherwise) explained. Depending on the standpoint of the ex pert, the model is either mainly retrospective - like Darwin's theory of natural selection as a model to explain the evolution of species - or it concentrates pro spectiveiy on the future by trying to predict events, e. g. catastrophes such as floods or droughts. Naturally, all these models are not perfect as they are man made, but they do help to solve problems. Politicians should draw consequences from these observations; but as they cannot be expected to evaluate such models, they need highly qualified advisers. This exposition already indicates that the terrn model encompasses many dif ferent facets with far-reaching consequences. We quote several examples in order to demonstrate the rather indefmite interpretation of the terrn and the various pur poses models are to serve; in fact we come to the conclusion that there are literally 'models everywhere'. Diverse as models are, they all share some common ideas such as the structural aspects of the modelling process. |

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### Contents

Models | 1 |

12 Etyma | 31 |

13 Purposes | 34 |

Systems | 46 |

22 Characterizing Systems | 49 |

23 Dynamic Systems | 63 |

24 Systems Analysis | 72 |

Mappings | 97 |

Tolerance | 228 |

82 The Quantitative Aspect | 234 |

Tests | 237 |

92 Terminology | 239 |

93 Testing | 242 |

Validity | 249 |

101 Validation | 250 |

102 The Scope | 251 |

32 Structure Preservation | 100 |

33 Chains and Invariants | 107 |

34 Morphisms | 111 |

Characterizing Models | 120 |

41 Contents | 121 |

42 Selection | 127 |

43 Projection | 134 |

The Art of Modelling | 139 |

51 Creating a Model | 142 |

52 Quality Criteria | 159 |

Inferences | 169 |

61 Deductive Inference | 171 |

62 Inductive Inference | 179 |

63 Personal Inference | 191 |

Probabilities | 195 |

72 Inductive Stochastic Inference | 198 |

73 Certainty and Prior Probability | 223 |

103 Epistemic Foundations | 257 |

104 Quantifying the Validity of a Model | 260 |

105 Evaluating a Model | 265 |

Suggestions for Further Reading | 267 |

References | 269 |

Appendix | 275 |

Modelling the Evolution of Galaxies | 279 |

Model Environments for an Early Alkaline Ocean | 309 |

Reconstructing the development of paleospecies | 323 |

The Modau Case Study | 335 |

Physical Modeling of a Glass Melter | 357 |

Modelling of Complexation Equilibria | 379 |

Weather Prediction by Numerical Modelling of Atmospheric Processes | 413 |

Simulation of Hydrogen Behaviour During a Nuclear Power Plant Accident | 435 |

List of Contributors | 457 |

### Common terms and phrases

adsorption analysis aspects balls Bayesian inference biological transmutations calculations catchment co-image co-model combustion complex components constant corresponding counter-image defined degree depends described determine distribution dynamic dynamic system elements equations evaluation event evidence evolution example experiments falsifying flood flow Forschungszentrum Karlsruhe further galactic galaxies goethite hominid Homo Homo habilis Homo rudolfensis hypothesis H inference input instance interacting galaxies interactions interpret Koobi Fora Lake Lake Van lead mapping mathematical means measured melter model liquid modelling process N-body N-body simulations natural numbers Nemrut Volcano NWP model object observed output parameters performance phenomena physical pictogram predictions prior probability probability problem proposition quantifier rational belief real numbers relations relevant represent representation respective scale scenario scientific Sect simulations solution speciation species structure Subsect subsystems surface swans temperature term theorem theory tion turbulent validity values verifying

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